Vol. 12, 1979
T h e Role of Activation Volume
the rich chemistry of a-chloro nitrones have resulted in the discovery of numerous synthetically significant
transformation^.^^
Conclusion We have attempted to show the development of a general methodology applicable to the synthesis of a variety of alkaloidal classes (e.g., the pyrrolizidine, quinolizidine, indolizidine, lycopodium, and tropane classes). The cycloadditions discussed are normally (69) G. E. Utzinger and F. A. Regenass, Helu. Chim.Acta, 37, 1892 (1954). (70) R.Bonnett, R. F. C. Brown, V. M. Clark, I. 0. Sutherland, and A. Todd, J . Chem. Soc., 2094 (1959). (71) J. J. Tufariello and E. J. Trybulski, unpublished observations. (72) (a) M. Petrzilka, D. Felix, and A. Eschenmoser, Helu. Chim.Acta, 56,9 (1973); S. Shatzmiller, P. Gygax, D. Hall, and A. Eschenmoser, ibid., 56,2961 (1973); S. Shatzmiller and A. Eschenmoser, ibid., 56,2975 (19731,
and references cited therein; E. Schalom, J-L. Zenon, and S. Shatmiller, J. Org. Chem., 42, 4213 (1977).
403
~ e l l - b e h a v e defficient ,~~ reactions. The inherent features of carbon-carbon bond formation, oxygen transfer, and nitrogen incorporation have been joined by the high site selectivities, regioselectivities, and stereoselectivities often observed in nitrone-alkene cycloadditions to render these reactions powerful weapons in the arsenal of the organic chemist. Indeed, it is our firm conviction that such processes will play an ever increasing role in the expansionary phase that is currently underway in organic synthesis. A n y success achieved in the program described herein must be attributed substantially to m y numerous productive and stimulating collaborators. T h a n k s f o r material support go t o the National Institutes of Health (GM 25303 and CA 14611) and the Research Foundation o f the State University o f N e w York. (73) However, see J. J. Tufariello and E. J. Trybulski, J. Org. Chem., 39,3378 (1974); E. Gossinger, R. Imhof, and H. Wehrli, Helv. Chim.Acta, 58, 96 (1975).
Role of Activation Volume in the Elucidation of Reaction Mechanisms in Octahedral Coordination Complexes GEOFFREY A. L A W R A N C and E " ~DONALD ~ R. S T R A N K S ~ ~ Department of Inorganic Chemistry, University of Melbourne, Parkville 3052, Australia Received April 18, 1979
The effect of pressure on the rate of a chemical reaction in solution, which can be attributed to a volume change occurring in the activation step, has been gaining recognition as an aid in mechanistic elucidation. The existence of a correlation between the main mechanistic features of a reaction and the activation volume is now widely accepted. Extensive studies of organic reactions using this technique have appeared.2 However, applications of the effect of pressure in the area of inorganic reaction mechanisms are still limited, though growing steadily. Advances in modern high-pressure techniques and equipment have made the measurement of the effect of pressure on reaction rate relatively simple. Activation enthalpies and entropies obtained from the effect of temperature on reaction rates can now be supplemented by activation volumes obtained from the pressure dependence of reaction rates. The interpretation of mechanism based on entropy change requires a structural concept involving inferred changes in both energy and nuclear position; volume change is based on changes in nuclear position only, and should therefore be inherently simpler to intercept. Geoffrey A. Lawrance was born in Ipswich, Australia, in 1948. He received his BSc. and Ph.D. degrees from the University of Queensiand, and a Dip.Ed. from the University of Melbourne. He held posts as Research Fellow at the university of Stirling (Scotland) and Senior Tutor and Lecturer at the University of Melbourne before taking up his present position as Research Fellow in the Research School of Chemistry at the Australian National university In 1978. Donald R. Stranks was born In Melbourne in 1929, and received MSc. and Ph.D. degrees from the University of Melbourne. He was Professor of Inorganic Chemistry at the University of Adelaide and then at the University of Melbourne before returning to Adelaide as Vice-Chancellor in 1977.
0001-4842/79/0112-0403$01.00/0
The activation volume ( A P ) for the generalized reaction aA bB + ... T* + CC + dD ... (1) can be defined as3 A T = -RT(a In k,/aP)T (2) which can also be written in terms of partial molar volumes (Vi) as AT = V T * - U V A- bVB - ... = - CUVA (3)
+
+
A
The reaction volume ( A P ) , or partial molar volume change for the reaction, can be expressed as A P = -RT(a In K / a P ) T (4 or A P =
(cV+ ~ ~ V +D...)
-
(UVA+ bVB + ...)
(5)
For convenience, it has become common practice to delete the bar over the volume symbol used to indicate partiality and, subsequently, activation volume will be symbolized by AV* and reaction volume by AVO. The activation volume can be calculated only from the effect of pressure on the rate constant and application of eq 2. The reaction volume can be determined by dilato(1) (a) Present address: Research School of Chemistry, The Australian National University, P.O. Box 4, Canberra 2600, Australia. (b) Office of the Vice-Chancellor, University of Adelaide, Adelaide 5001, South Australia. (2) T. Asano and W. J. le Noble, Chem. Rev., 78, 407 (1978). (3) M. G. Evans and M. Polanyi, Trans. Faraday Soc., 31,875 (1935).
0 1979 American Chemical Society
Lawrance and Stranks
404
metry, by measuring the effect of pressure on the equilibrium constant K , or by combination of separately determined partial molar volumes of all reactants and products in eq 6. The exact theoretical relationship between rate and pressure and equilibrium constant and pressure is not known; hence the calculation of AV must be empirical in nature. Frequently, but not always, AV itself shows a pressure dependence; the slopes of In h p vs. P graphs then decrease with increasing pressure. The most popular empirical equation is a quadratic of the form4 In k p = In ko 4 bP + cP2 (7) Despite the fact that the shape is not realistic (it demands an extremum) at very high pressures, eq 7 accurately describes a variety of reactions a t the moderate pressures employed in most experiments. From eq 7, the activation volume a t any pressure is given as AV’p = -bRT - 2RTcP (8) and the generally quoted volume of activation at zero pressure is AV* = -bRT (9) AV is positive when the rate decreases upon the application of pressure and negative when the rate increases with increased hydrostatic pressure. It is frequently possible to determine AV* with uncertainties of less than f l c m 3 molw1,and it is now clear that AV* is usually determined more reliably than AS*. The pressure dependence of the activation volume, from the curvature in the In hp vs. P graph, can be represented by a term called the compressibility coefficient of activation (Apt), defined by eq 10. We can A@* = - ( a A V / a P ) , = 2RTc (10) also express A@*in terms of the difference in compressibility coefficients (p) of the transition state and all reactants as A@* = ( - a v * / a P )-~ Ca(aV,/aP), (11) A
= P*
-
(12)
CaPA A
A further term sometimes employed is the similarsounding compressibility of activation (AK’), simply defined as AK* = .lp*/AV*
(13)
It is convenient for a simplified analysis of activation volumes to consider octahedral coordination complex ions as essentially incompressible spherical species with a characteristic average r a d i ~ s . ~It, has ~ been assumed that a five-coordinate intermediate (NIL,) arising from dissociative release of a neutral ligand (L) will occupy the same volume as its six-coordinate precursor (ML6).5 The volume of Ni(NH3)62+(138 cm3 mol-’) is identical with that calculated for the hypothetical Ni(NH3)52+ ~ a t i o n .For ~ the analogous cobalt(II1) system, the intermediate C O ( N H ~ )has ~ ~been + recently estimated7 to have the same volume as C O ( N H ~ ) ~ ~=+ 55 cm3
(v
(4)H. S. Golinkin, W. G. Laidlaw, and J. B. Hyne, Can. J . Chem., 44, 2193 (1966). (5) D. R. Stranks, Pure Appl. Chem., 38, 303 (1974). (6) N. S. Hush, Discuss. Faradav Soc., 26, 154 (1958). (7) D. A. Palmer and H. Kelm, inorg. Chem., 16, 3139 (1977).
Accounts of Chemical Research
Table I Partial Molar Volume and Compressibility Coefficient of Water in Bulk and Electrostricted Environmentsa
a
V,
p , c m 3 mol-’
environment
c m 3 mol-’
kbar-’
bulk solvent second hydration layer first hydration layer coordination sphere
18.0 15.6 15.0 14 + 15
0.84 0.22 0.12 0.06 --t 0.12
Estimated for a 3+ ion.
mol-I). For an associative mechanism, the seven-coordinate intermediate (ML,) formed by incorporation of a ligand may likewise occupy approximately the same intrinsic volume as its precursor ML6. Subsequently, for neutral ligands L, the dissociative mechanism is expected to lead to a transition state (ML5 L) of greater volume than the ML6 precursor (positive AV); the associative mechanism should produce a transition state (ML,) of less volume than the combined volumes of ML6 and L (negative AV*). Since we are dealing generally with the reactions of ionic species in solution, it is most important to appreciate that the partial molar volume of a complex ion involves two major components. The first is the intrinsic volume (Vintr)arising, in the case of complex cations, from the bulk of groups within the coordination sphere. However, the electrostatic interaction of the charged ion with the solvent (Vel)is also significant. An ion introduced into a solvent causes a significant contraction of the system; this is termed electrostriction of the solvent. Since the entering or leaving groups are commonly charged, the electrostrictive effect should not be neglected. In terms of the activated state, we may, therefore, partition AV into intrinsic and electrostrictive components. The latter effect may frequently be the dominant contributor to the experimentally determined activation volume. A consequence of electrostriction is the formation of ordered layers of solvent molecules, or solvation spheres, about a charged complex ion. Both the partial molar volume and compressibility coefficient of the solvent vary on transition from “bulk” solvent to solvation sphere or coordination ~ p h e r e . ~The ? ~ relevant variation for water is shown in Table I. subsequently, reactions of ionic complexes which exhibit a marked pressure dependence of AV itself (Le., A@* # 0) commonly exhibit dominant electrostrictive contributions to AV. The preceding discussion has generally been based on octahedral metal ions. It is in these complexes that we have been principally interested, and this Account is restricted to a discussion of complexes of this type. Further, the relative insensitivity of most physical properties of water to applied pressureg and its prominence in solution kinetics make it an excellent choice of solvent for our purposes; most of the systems discussed will involve aqueous solutions. The type of reactions which we have been investigating can be followed conveniently by the use of apparatus pressurized routinely to at least 1720 bar (25000 psi). This pressure range is sufficient to determine AV with acceptable accuracy for most reactions. One technique employs a sampling vessel fitted with a high-pressure tap which
+
(8) E. Whalley, J . Chem. Phys., 38, 1400 (1968). (9) S.D. Hamann, “Physico-Chemical Effects of Pressure”, Butterworths, London, 1957.
The Role of Activation Volume
Vol. 12, 1979
allows aliquots to be withdrawn at appropriate intervals. These aliquots are then immediately subjected to some physical measurement to ascertain the reaction rate. We have employed this technique in studies of racemization reactions. The alternative method is to follow the rate of reaction spectrophotometrically in situ using a high-pressure spectrophotometer cell with sapphire windows.1°
Table I1 Activation Volumes and Entropies f o r Selected Racemization and Geometrical Isomerization Reactions of ' Octahedral Complexesa A
complex
characterized by isotopic exchange studies for Ni(phen)z+, a suitable example of this type of mechanism.16 Two different types of intramolecular mechanisms can be considered for complexes with bidentate ligands and are differentiated by whether racemization occurs with or without bond rupture.15 A one-ended dissociation (eq 15) involves bond breaking of one chelate bond A
accompanied by rearrangement to a five-coordinate transition state. Alternatively a twist mechanism (eq 16) proceeding without bond rupture by way of an inactive trigonal prismatic transition state can be considered. Although the partial molar volume of each optical isomer will be identical (i.e., AVO = 0), the partial molar volume of the transition state need not be the same as that of the precursor. If we assume that the five-coordinate intermediate volume is changed only because of (10)
F.K. Fleischmann, E. G. Conze, D. R. Stranks, and H. Kelm, Reu.
Sci. Instrum., 45, 1427 (1974). (11) G. A. Lawrance and D. R. Stranks, Inorg. Chem., 16,929 (1977). (12) G. A. Lawrance and D. R. Stranks, Inorg. Chem., 17,1804 (1978). (13) G. A. Lawrance, D. R. Stranks, and S. Suvachittanont, Inorg. Chem., 17, 3322 (1978). (14) G. A. Lawrance, S. Suvachittanont,D. R. Stranks, P. A. Tregloan, L. R. Gahan, and M. J. O'Connor, J. Chem. Sac., Chem. Commun., in press. (15) N. Serpone and D. G. Bickley, Prog. Inorg. Chem., 17, 392-566 (1972). (16) F. Basolo, J. C. Hayes, and H.M. Neumann, J . Am. Chem. SOC., 75,5102 (1953); R. G. Wilkins and M. J. G. Williams, J. Chem. Soc., 1763 (1957).
v',
AS*,
c m 3 mol-' Racemization - 1 6 . 3 i 0.4 -12.3 i 0 . 3 -12.0 i 0.3 -1.5 i 0.3 -1.0 i 0.2 + 3 . 3 i 0.3 + 3 . 0 i 0.3 + 1 5 . 6 t 0.3 -1.5 t 0.3 -0.1 i. 0.1 -5.2 i 0.5b -1.9 i 0.2= + 9 . 8 i 0.4d t 7 . 8 i 0.4e + 5 . 2 i 0.3f c 5 . 4 i. 0.3g
Experimental Applications Racemization Reactions. Prior to 1977, no activation volumes had been reported for racemization reactions of octahedral complexes in solution, despite the continuing interest in these systems in the chemical literature. Subsequent to our first report,ll several other studies have appeared.12-14 Both intermolecular and intramolecular mechanisms have been proposed for racemization in octahedral chelate ~omp1exes.l~The intermolecular mechanism (eq 14), involving complete loss of one chelate, has been R
405
Isomerization -16.6 i 0.5 (-1.8)h trans-Cr(mal),(OH,); +8.9 i 0.3 trans-Co(en),+ 7 . 5 i 0.2 (Se03H)(OH,)2+ t r a n ~ - C o ( e n ) , ( O H , ) , ~ + 1 4 . 3 F 0.2 trans-Cr(ox),(OH,),-
(+Lop
trans-Co(en),(CH,COO)(OH,)*+ trans-Co( en),(SeO3)(OH2)f trans-Co( en),(OH)(OH2)2+
J K - ' mol-' -762 -69i -79i -64t -695 -561 -63i t8dt +12t +7 i +16+ +13+ +18c +51i +35i
ref
8
11
7 9 6 4
11 11 11 11 11
8 8
3 20 12 12 12 25 10 +11+ 12
11 12 12 13 13 13 14 14 14 14
-61
i
5
21
+74 +53
i i
5 4
21 5,20
+lo3
i
5
19
t
9
22
8
+7.9
i.
0.3
+61
+7.3
F
0.2
+36i I
+14.5
i
1.1
+lo0
i
20
5 , 20
20
a Determined in dilute aqueous acid exce t where indicated. 1.0 M acid. 0.01 M acid. Ethanol. @ Toluene. Dimethylformamide. g Acetonitrile. Nonzero Ap *, c m 3 mol-' k b a r - ' , in parentheses.
h?
motion of the leaving group out of the first coordination sphere, the one-ended dissociative mechanism in the case of a neutral ligand should lead to a transition state of greater volume than its precursor due to this extension of the dangling arm into the solvent. Hence a positive AV is predicted. When the dissociated arm is charged, however, solvent electrostriction of the new charge center will dominate, causing an effective decrease in volume; hence a negative AV is then expected. To a first approximation, since a twist mechanism in the absence of any spin-change preequilibrium can be assumed to occur without bond extension and only with bond angle distortions, no change in volume in the transition state is predicted, and hence AV should be zero. The first study of intramolecular racemization at elevated pressures, that of the chromium(II1) complexes Cr(aa)3-n(~~),(3-2n)f (aa = 2,2'-bipyridyl (bpy or 1 , l O phenanthroline (phen); ox2- = oxalate; n = 1 3), produced a clear mechanistic differentiationell Large negative AV values for Cr(ox)$- and Cr(ox)(aa),- contrasted with near-zero AV for the remaining reactions (Table 11). These disparate AV have been interpreted in terms of a one-ended dissociative mechanism with a dangling ligand for the former complexes and a twist mechanism for others. A great deal of evidence has established a dissociative intermolecular mechanism for racemization of Ni(phen)32+(eq 14).16 The AV for racemization1*is -1.5
-
406
Lawrance and Stranks
cm3 mol-', which cannot be readily reconciled with an intermolecular mechanism. However, AV for racemization and aquation are identical, as expected, and arguments relating to solvation effects or bond length changes of coordinated ligands in the transition state have been presented to account for the small A V . The mixed-ligand complexes N i ( ~ h e n ) ~ ( b p yand ) ~ + Ni(phen)(bpy)?+ also show small AV (Table II).13 While the rigid phen ligand cannot participate in a one-ended dissociation for steric reasons, the bpy ligand can twist about the C(2)-C(2') bond linking the pyridine rings. The acid dependence of AV observed, particularly with Ni(phen)(bpy)?+, is consistent with the favored mechanism, where protonation of the one-ended dissociated bpy ligand can occur. A similar acid dependence of 4V is observed for aquation of Fe(bpy)32+,where an analogous mechanism is favored. Small AV observed for the nickel complexes are consistent with the expectation of the chelated and partly dissociated bpy ligands sweeping out similar volumes. Interpretation of AV for racemization of Fe(phen)?+ is complicated by a significant positive contribution, estimated as approximately 9 em3 mol-l, from a preequilibrium excitation from the low-spin ground state to a high-spin state with concomitant general metalligand bond lengthening.12 The moderately small residual component of AV* could be consistent with the previously proposed twist mechanism. Some preliminary studies of the pressure dependence of racemization of n e u t r a l tris(dithi0carbamato)cobalt(III)complexes in a range of nonaqueous solvents have been c0mp1eted.l~The positive AV values determined with the pyrrolidine chelate (pdtc) in several solvents (Table 11) are not consistent with either a one-ended dissociative mechanism for a negatively charged ligand or with a simple twist mechanism. However, a spin preequilibrium prior to a twist process, such as that proposed for racemization of Fe(phen)32+, would account for the positive AV*. The observation that AV and AK*are not appreciably solvent dependent supports a twist mechanism, as does NMR evidence for a related system.17 It is possible that twisting motions may be more facile in the proposed "expanded" highspin transition state. Such a spin preequilibrium can be expected to make substantial positive contributions to both AV* and AS'. Geometrical Isomerization Reactions. The first activation volumes for geometrical isomerization of octahedral complexes were reported in 1972,18and accelerated interest in this area has subsequently led to a number of similar s t ~ d i e s ~ (Table J % ~ ~11). Mechanisms that can lead to geometrical isomerization are analogous to those that may lead to racemi~ation.'~For complexes of the type M(aa)2L2n+(aa = bidentate ligand), dissociative, twist, or associative mechanisms can be consid(17) M. C. Palazzotto, D. J. Duffy, B. L. Edgar, L. Que, and R. H. Pignolet, J. Am. Chem. SOC.,95, 4537 (1973). (18) E. G. Conze, H. Steiger, and H. Kelm, Chem. Ber., 105, 2334 (1 ~ 9731 - .--,. (19) D. R. Stranks and N. Vanderhoek, Inorg. Chem., 15, 2639 (1976). (20) A. D. Fowless, D. R. Stranks, T. R. Sullivan, and N. Vanderhoek, to be published. (21) P. L. Kendall, G. A. Lawrance, and D. R. Stranks, Inorg. Chem., 17, 1166 (1978). (22) G. A. Lawrance and S.Suvachittanont, J . Coord. Chem., 9, 13 (1979). (23) Y. Kitamura, Bull. Chem. SOC.Jpn., 49, 1002 (1976). (24) T. R. Sullivan, Ph.D Thesis, University of Melbourne, 1978.
Accounts of Chemical Research
ered. One-ended dissociation of a bidentate ligand (eq 17), dissociation of a unidentate ligand (eq 181, twisting ?
0
0
0
0
0
0
0
0
CO
"I
I
0
(eq 19), or an associative mechanism (eq 20) can lead to isomerization. Unlike racemization reactions the partial molar volumes of the geometric isomers need not be the same, and both AvO and A V may be nonzero. Predicted A V generally follow arguments developed in the earlier section. In the case of dissociative aquo ligand release, complete release into the first solvation sphere would involve in the upper limit a positive contribution due to the intrinsic volume of water in that environment of +15 cm3 mol-'. This analysis assumes that the five-coordinate intermediate retains the same volume as its precursor, and that solvation of the ionic precursor and transition states are similar for a neutral leaving group. The arguments for an associative mechanism are the reverse of the above, leading to a predicted upper limit to AV* of -15 em3 mol-l. The success of AV in the elucidation of mechanisms of geometrical isomerization is exemplified by a study of trans- eis-Cr(aa)z(OHz)z-for aa2- = oxalate (AV' = -16.6 cm3 mol-') and aa2- = malonate (AV* = +8.9 cm3 A V for the former complex is consistent with the established mechanism of one-ended dissociation of a chelated oxalate and similar to AV* for racemization of Cr(ox)$- which proceeds via the same mechanism." The markedly different A V for the malonate complex provides definitive evidence for a different mechanism, and release of an aquo ligand in the transition state (eq 20) is favored in this case. Studies of a series of reactions of the type transcis-Co(en)2(OH2)(X)"+(en = 1,2-diaminoethane; X = OH2,Se03H-, Se032-,CH3COO-) have provided positive AV values in each case, consistent with a general dissociative mechanism of aquo ligand r e l e a ~ e . Varia~,~~ tion in the size of 4V and AD* (Table 11) may indicate minor mechanistic differentiation. Complete dissociative release of a water molecule from the coordination sphere to the bulk solvent (characterized as a D mechanism) should lead to larger 4V and Ap* than for water interchange between the coordination and first solvation spheres (an Id mechanism). There are some grounds for assigning a D mechanism for the X = OH2 complex and an Id mechanism for the others on the basis of this analysis,22although the extraction of such detail from
-
-
The Role of Activation Volume
Vol. 12, 1979
Table I11 Activation a n d Reaction Volumes for Selected Hydrolysis Reactions of Octahedral Complexes ~ p * , c m ~A V O , AV*, c m 3 mol-' cm3 complex mol" kbar-' mol-'
ref
Aquation: Unidentate Ligandsa Co( NH,),(Cl)'+ -10.6 t 0.4 -2.1 t 0.2 -11.6 Co( NH,),(Br)'+ -9.2 t 0.2 -2.0 t 0.2 -10.8 -18.5 t 0.7 -4 t 0.5 -19.2 CO(NH,)~(SOZI)' 0.0 0 CO(NH,),(OH,)~+ +1.2 i: 0.1 Cr(NH3),(OH2)3+ -5.8 c 0.2 0 0.0 Cr(NH,),(Cl)*+ -10.8 t 0.3 -1.0 t 0.2 -8.4 -10.2 0 . 3 -1.0 fi 0.1 -8.4 NH3) 5 ( Br)' + Co(NH3),(Me,S0)3+ -1.7 i: 0.7 0 0 C o ( N H , ) , ( ~ r e a ) ~ + +1.3 t 0.5 + 3 . 5 t 0.3 0 Co(dmg),Cl(urea) trans-Co( d t c d ) t 8 . 7 + 0.4 0 (N,)C1+ +_
Aquation: Bidentate Ligandsb trans-Cr(ox),+1.7 t 0.7 0 ._ ( 0 H 2 1;+ 2 . 4 t 0.6 0 trans-Crf mall,,* ( 0 H, 1 Fe( phen) 3 2 + + 1 5 . 4 . t 0.3 0 W b P Y )3' + -1-11.5 t 0.7 0 Ni(phen),'+ -1.2 t 0.2 0
;-
Base Hydrolysis t 8.5 Co( NH,),Br2 +19.5 t 1.1 +9.5 r 2.2 Co(NH,),(SO,)+ + 2 8 . 9 t 2.2 +7.7 t 2.1 Co(NH3)5(P04) Co(NH,)5(ONO)ZtC t 2 7 . 0 + 1.4 + 4 t 2 +
Dilute aqueous acid. >1.0 M aqueous acid. catalyzed linkage isomerization.
29 29 29 30 31 28 28 7 35 34
36
21 21 37 24 12
38 5 5 40 Base-
activation volume data a t present should be treated with some reserve. Examination of data in Table I1 indicates that there is a correlation between AV and AS* in most cases. Such an expected relationship has been reported prev i o u ~ l ymost , ~ ~ recently for aquation reactions of inert complexes.26 Since positional changes in the transition state contribute to both AV and AS* in the same sense, a correlation is likely; however, an exact relationship is not necessary as rotational contributions to AS*, for example, need not contribute to AV. An analysis of the available data for racemization and geometrical isomerization of octahedral complexes in solutionz7indicates that a fairly good linear relationship is obtained except for the racemization of Cr(aa)33+and Cr(aa)z(ox)' (aa = phen or bpy) which are predicted to involve a simple trigonal twist mechanism; this twist mechanism is expected to lead to a negative AS* and a zero AV*. Least-squares analysis of all available data predicts a small positive AS* for a near-zero AV. This is observed in the racemization of N i ( ~ h e n ) ~in~ + which , case there is firm evidence for a dissociative intermolecular mechanism rather than a twist mechanism. Absence of a correlation of AV and AS* for racemization and isomerization may, therefore, be indicative of a twist mechanism. Hydrolysis Reactions. Two of the first systematic studies of activation volumes for metal complexes reported aquation reactions of series of C O ( N H ~ ) ~and X~+ of C r ( N H 3 ) P +complexes (Table III).z8~BDetermined (25) D. T. Y. Chen and K. J. Laidler, Can. J . Chem., 37,599 (1959). (26) M. V. Twigg, Inorg. Chim. Acta, 24, L84 (1977). (27) 6.A. Lawrance and S. Suvachittanont,Inorg. Chim. Acta, 32, L13 (1979). (28) G. Guastalla and T. W. Swaddle, Can. J. Chem., 51, 821 (1973).
407
AV and AV" were interpreted in terms of dissociative and associative character, respectively. The value of using AV" in conjunction with AV for mechanistic elucidation in these systems has recently been clearly presented by Kelm.7 The contrast between the dissociative reactions of cobalt(II1) and the apparently associative reactions of chromium(II1) is most conveniently illustrated by AV for solvent exchange in the aquo c o m p l e x e ~ , ~ ~with 1 ~ ' AV* = +1.2 cm3 mol-l for Co(NH3)5(OH2)3+but AV = -5.8 cm3 mol-' for Cr(NH3)5(OH2)3+.Aquo exchange in c i s - C ~ ( e n ) ~ ( O H ~ ) ~ ~ + similarly proceeds32with AV = +5.9 cm3 mol-', while a AV = -9.3 cm3 mol-l has been reported33for exchange in Cr(OHz)63+.Since release of a neutral ligand can be anticipated to produce very small volume changes of an electrostrictive n a t ~ r ea, ~positive AV is diagnostic of a dissociative mechanism and a negative AV diagnostic of an associative mechanism above. The situation in reactions where release or displacement of a charged ligand occurs in the transition state is complicated by significant electrostrictive contribution to AV in addition to intrinsic volume changes. This can be seen from comparison of AV for aquation of C O ( N H ~ ) ~ ( S O Co(NH3)5Clz+, ~)+, and C O ( N H ~ ) ~ (Me2S0)3+,for which values of -18.5, -10.6 and -1.7 cm3 mol-l, respectively, are obtained as the charge on the leaving group varies from 2- to 1- to 0. The role of the nonleaving groups in determining the size and sign of AV has not yet been subjected t o extensive investigation. Aquation of the formally neutral complex C ~ ( d m g ) ~ ( u r e a ) C(dmg l = dimethylglyoximato-) occurs with loss of 0-bound urea. A AV of +3.5 cm3 mol-' is consistent with a dissociative mechanism, the small size suggesting an interchange (Id) mechanism.34 A AV of +1.3 cm3 mol-l has been observed for aquation of urea in the C ~ ( N H ~ ) ~ ( u r e a ) ~ + cation. The similarity of AV in the two complexes of different charge but identical neutral leaving group is consistent with minor contributions only from change in solvation of the ground and transition states.35 AV for chloride aquation in trans-Co(dtcd)(N3)C1+(dtcd = 5,12-dimethyl-1,4,8,ll-tetraazacyclotetradeca-4,11diene) is36+8.7 cm3 mol-', in contrast to a AV of -10.6 cm? mol-l for aquation of C O ( N H ~ ) ~ CThis ~ ~ +positive . AV is certainly consistent with the accepted dissociative mechanism. However, the significant variation from the value for C O ( N H ~ ) ~suggests C ~ ~ + that the large, bulky macrocycle may determine that electrostrictive solvation of chloride ion is less marked in that complex than in the pentammine complex, even when substantial bond stretching has occurred. Hydrolysis reactions involving release of bidentate rather than unidentate ligands (Table 111) are often complicated by the possibility of several stepwise pathways for hydrolysis which nevertheless yield a similar (29) W. E. Jones, L. R. Carey, and T. W. Swaddle, Can. J. Chem., 50, 2739 (1972). (30) H. R. Hunt and H. Taube, J . Am. Chem. SOC.,80, 2642 (1958). (31) T. W. Swaddle and D. R. Stranks, J. Am. Chem. SOC.,94, 8357 (1972). I____,_
(32) S. B. Tong, H. R. Krouse, and T. W. Swaddle, Inorg. Chem., 15, 2643 (1976). (33) D. R. Stranks and T. W. Swaddle, J . Am. Chem. SOC.,93,2783 (1971). (34) S. Suvachittanont and G. A. Lawrance, J . Sci. SOC.Thailand, 4, 52 (1978). (35) G. A. Lawrance, unpublished data. (36) G. A. Lawrance and S. Suvachittanont,submitted for publication.
408
Lawrance and Stranks
Accounts of Chemical Research
AV. Some mechanistic information can still be forthcoming. For example, the essentially identical AV for acid-catalyzed aquations of C O ( O X ) ~ ( O H(+1.7 ~ ) ~ -cm3 mol-l) and Cr(mal)2(OH2)2-(+2.4 cm3 mol-') are consistent with one mechanism operating for both aquation reactions, in contrast to the different mechanisms established for geometrical isomerization of these complexes from AV* data.21 Aquation of F e ( ~ h e n ) and ~~+ Fe(bpy)z+ both show large positive AV, consistent with dissociative release of a neutral hel late.'^,^^,^^ Some activation volumes have been reported for base hydrolysis reactions (Table III).5138 In terms of the favored conjugate base mechanism for base hydrolysis, one may write
most consistent with dissociative release of an aquo ligand as the prime feature of an Id mechanism, and they contrast with the apparently associative character of oxalate interchange reactions of C I - ( O H ~ ) which ~~+ exhibit negative AV* values.43 The reaction of Fe(CN)5(3,5-Me2py)3with cyanide, pyrazine, or imidazole and of F ~ ( C N ) & ~ - C N - with P~)~cyanide yield an average AV of +20.6 (h0.4) cm3 mol-' (py = pyridine).44 The large, positive, and nucleophile-independent nature of AV* is strong evidence for a dissociative (D) mechanism, with effective dissociation of the neutral leaving group from the Fe(CN)$- moiety in the transition state. The similarity in AV* despite substitution by a charged or neutral ligand indicates that the incoming group does not participate signifi(H3N)CoA4Xn+ -I- OH- + (H~N)COA~X('-')+ + HzO cantly in the transition state; otherwise different elec(21) trostrictive contributions to AV* would reasonably be expected for the charged and neutral nucleophiles. (H~N)COA~X(~-')+ (+H2O) A recent study of the nucleophilic substitution of (H~N)COA~(OH ~ + (22) +)X"Fe(phen):+ and Fe(bpy),2+with hydroxide and cyanide ion indicates a similar primarily dissociative mechanism Contributions from both charge neutralization of hymay be operatingS4j The AV values of approximately droxide ion on formation of the conjugate base (eq 21, +20 cm3 mol-l in each reaction are independent of nuAVcB) and from further intrinsic and electrostatic volcleophile. Either an associative mechanism or a mechume changes on release of X"- (eq 22, AVIX) are exanism of direct nucleophilic attack initially on the unpected. Despite the change in overall charge on the saturated chelate46would require appreciable desolvacomplex ion on forming the conjugate base, the AV,, tion of the attacking nucleophile from both steric and contribution may approach the volume of electrostriccharge neutralization considerations. The hydroxide tion for OH- ( t 2 2 cm3 since ions such as Coion exhibits a large volume of electrostriction of 22 cm3 (NH3)5(OH2)3+ and C O ( N H ~ ) ~ ( O H have ) ~ +similar parmol-' compared to 8 cm3 mol-' for the cyanide ion.39 tial molar volume^.^ The generally positive AV* obSince the intrinsic volumes of the ions are similar,44 served to date are consistent with a large hVcBcontriboth mechanisms should produce positive but distinctly bution, which is only partially offset by contributions different AV* for the different nucleophiles. The obfrom leaving group release (Table 111). A conjugate base servation of positive pressure- and nucleophile-indemechanism has also been identified recently in the hV* values does not favor either of these albase-catalyzed isomerization of C O ( N H ~ ) ~ ( O N O ) ~ +pendent ,~~ ternate mechanisms. where a positive AV of +27 cm3 mol-l contrasts with Redox Reactions. Two mechanisms for oxidationa AV of -6.7 cm3 mol-' previously reported41 for the reduction involving electron transfer can be considered spontaneous linkage isomerization. for metal complexes. The outer-sphere mechanism inThe concept of a relationship between AV* and AS' volving electron transfer without bond-making or has been introduced previously.2k27 A correlation has breaking lends itself to a relatively straightforward already been discussed above for racemization and geotreatment in predicting AV via the quantitative adiametrical isomerization, and recently a linear correlation batic theories of Marcus.47 A detailed analysis of these for aquation reactions of inert complexes has also been calculations for a series of electron-transfer systems has presented.26 It should be emphasized again that an been provided in an earlier reviewe5 The success of exact relationship should not be inferred, nor is it comthese calculations can be exemplified by the established monly observed. outer-sphere reaction between C ~ ( e n )and ~~C +~(en)~~+ Substitution Reactions. Several reactions involving which produced a AV (experimental) of -19.8 cm3 substitution by ligands other than water have been compared with a calculated value of -18.4 cm3 studied in which AV have provided mechanistic inform01-I.~~ For the Fe2+as/Fe3+, exchange, the experimation. The interchange reactions42of ion pairs cismental AV of -12.2 cm3 mol-9 again is similar to the C O ( ~ ~ ) ~ ( O H ~ ) ~ + - H ~ Cto~ yield O ~ / Co(en),(ox)+ HC~O~and of c i s - C ~ ( e n ) ~ ( O(OH2)2+.C2042H) to C ~ ( e n ) ~ - calculated value of -14.4 cm3 mol-l, indicating an outer-sphere mechanism. By contrast, the Fe2+/Fe(OH)2+ (OH)(C204)exhibit a common pressure-independent and Cr2+/Cr3+aqueous systems exhibit experimental AV* of +4.7 cm3 mol-' which is similar to that obAV* which do not agree with predicted 4 V * and have served32 for exchange of solvent water in trans-Cosubsequently been assigned inner-sphere mecha(er.~)~(oH,)$+ of +5.9 cm3 mol-l. These observations are nisms,5,48 +
(37) J.-M. Eucie, D. R. Stranks, and J, Burgess, J . Chem. Soc., Dalton Trans., 245 (1975). (38)C. T. Burris and K. J. Laidler, Trans. Faraday Soc., 51, 1497 (1955). (39) S.D. Hamann, Div. Appl. Chem. Tech. Paper No. 3, C.S.I.R.O. Aust., 1972. (40) W. G. Jackson, G. A. Lawrance, P. A. Lay, and A. M. Sargeson, Inorg. Chem., in press. (41) M. Mares, D. A. Palmer, and H. Kelm, Inorg. Chim. Acta, 27,153 (1978). (42) D. R. Stranks and N. Vanderhoek, Inorg. Chem., 15. 2645 (1976).
(43) C. S. Schlenk and H. Kelm, J . Coord. Chem., 2, 71 (1972). (44) T. R. Sullivan, D. R. Stranks, J. Burgess, and R. I. Haines, J. Chem. Soc., Dalton Trans., 1460 (1977). (45) 6 . A. Lawrance, D. R. Stranks, and S. Suvachittanont, Inorg. Chem., 18, 83 (1979). (46) R. D. Gillard, Coord. Chem. Rev., 16, 67 (1975). (47) R. A. Marcus, J . Chem. Phys., 24, 966,979 (1956); 26,867 (1957); Discuss. Furaday Soc., 29, 129 (1960). (48) W. H. Jolley, N. Vanderhoek, and D. R. Stranks, unpublished data.
Nonelectrolyte Solubility Theory
Vol. 12, 1979
An inner-sphere mechanism involves electron-transfer via a bridging ligand, as exemplified by the system
-
(NH3)5CoX2++ Fe2+aq [ (NH3).&O~+--X-*.F~~+,~]* ( N H ~ ) & o ( O H ~+ ) ~FeX2+aq + +
Should such a reaction proceed by an outer-sphere mechanism a negative AV is predicted. Observed values of +11 (X = F-), +8 (X = C1-, Br-), and +14 (X = N3-) em3 mol-1 have been interpreted in terms of an inner-sphere mechanism with appreciable desolvation of the charged species in the transition state contributing positively to the experimental AV*.49 Recently, activation volumes for reduction of Co(NH3)&12+by iron(I1) in the presence of sulfate ion show the influence of an iron(I1) sulfate pre-equilibrium with a significant variation of AV observed for varying Fe(S04)aq/Fe2+aq ratios.50 This variation is consistent with inner-sphere reduction by two separate pathways with FeZfaqor Fe(SOdaq-
Concluding Remarks While the topics discussed above encompass recent research endeavors within our laboratories for the application of activation volumes to mechanistic elucidation in reactions of octahedral metal complexes, we can expect the technique to continue to be applied to new areas of mechanistic interest in the future. Although definitive mechanistic evidence will not always be (49) J. P. Candlin and J. Halpern, Inorg. Chem., 4, 1086 (1965). (50) S.Suvachittanont, J. Sci. Soc. Thailand, 3, 118 (1977).
409
forthcoming from activation volumes, there is now a sufficient body of experimental data accumulating to allow useful mechanistic information to be gleaned from most studies. Certainly activation volume is proving superior to activation entropy as a general mechanistic guide, since AV is usually determined with good precision, and the concept of a volume difference between initial and transition state is amenable to simple mechanistic modelling. The principal and sometimes severe difficulty in interpretation or prediction of AV lies in an assessment of the size of any electrostrictive component. Since we are usually dealing with ionic species and often with motion of charged ligands in the activation step, electrostrictive components can dominate intrinsic components. It is likely future investigations of the role of the nonleaving groups in series of complexes with common leaving group and metal ion may aid our understanding of electrostrictive effects. Further, studies in a range of both protic and aprotic solvents, where solvation effects should vary considerably, should be of value. Few applications in reactions of organometallic compounds have been reported, and some expansion in this area would be welcome. The increasing body of experimentally determined activation volumes and reaction volumes, combined with their value in mechanistic elucidation, presage a continued expansion in the study of reactions at elevated pressures in the area of conventional kinetics which is our prime interest. The investigations of activation volumes for octahedral coordination complexes offer more detailed insights into the actual molecular rearrangements occurring during their reactions.
A Modern Approach to Nonelectrolyte Solubility Theory SAULGOLDMAN Guelph- Waterloo Center for Graduate Work in Chemistry, Guelph Campus, Department of Chemistry, University of Guelph, Guelph, Ontario, Canada N l G 2WI Received July 16, 1979
People get interested in solubility theory for one of two reasons. Engineers and applied scientists see it as a means of predicting solubilities in those systems for which data are wanted, but do not exist, and are impractical to obtain. Those among us with more theoretical inclinations would like to know, from the basis of intermolecular forces, why, at any specified temperature and pressure, one substance dissolves in another to exactly the extent that is observed. In this Account we deal with the theoretical aspects of solubility theory; Professor Goldman's research interests include thermodynamics and the application of equilibrium statistical mechanics to liquids and solutions. He was born in Montreal in 1943 and received his BSc. and Ph.D. degrees from McGiIi. On receiving the Ph.D. (1969) he was awarded the Ambridge price-given annually at McGili to the top-ranking Ph.D. student in science or engineering. From 1969 to 1972 he was a NRC of Canada postdoctoral fellow at the University of Florida in Gainesvliie. Since 1972 he has been a faculty member in the Chemistry Department at the University of Gueiph.
0001-4842/79/0112-0409$01.00/0
in particular, after a preliminary comment we do four main things. First we will go through a bit of history, and in the process point out those early ideas that have found a lasting place in solubility theory. Then we show how recent advances in the theory of liquids has made it possible to quantitatively predict solubilities and related functions from intermolecular forces without using any adjustable parameters. Calculations of this kind, even for the very simple systems we describe, were not possible prior to about a decade ago. Following this we show how these calculations can be used both in an approximate way to interpret solubility data in complex systems and in a rigorous way to intercompare theories and to elucidate the influence on solubility made by previously neglected phenomena such as quantum effects and nonadditive intermolecular forces. Finally, we outline some of the remaining problems in the field
0 1979 American Chemical Society
